{
  "abstract": "We study the second shape derivative of an optimal design functional involving a nonlocal term in order to prove rigidity of the ball. Our approach relies on a continuity argument that relates the second variation to that of the corresponding local problem. The model serves as a prototype for a broader class of shape optimization problems to which the same strategy may be adapted.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29958",
  "author_total": 3,
  "authors": [
    {
      "name": "Dario Mazzoleni"
    },
    {
      "name": "Riccardo Moraschi"
    },
    {
      "name": "Berardo Ruffini"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bef3g91h910t7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29958",
  "fulltext_url": null,
  "id": "bef3g91h910t7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.29958",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7223213789",
  "pdf_url": "https://arxiv.org/pdf/2610.29958",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bef3g91h910t7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.29958",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29958"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Rigidity of the ball for Hartree-type energies and second shape derivative via a continuity argument",
  "title_text": "Rigidity of the ball for Hartree-type energies and second shape derivative via a continuity argument",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/bef3g91h910t7",
  "venue": "arXiv",
  "versions": []
}